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Linear-Exponential Loss (per observation)

Source: R/regr_linex.R
linex.Rd

Measure to compare true observed response with predicted response in regression tasks.

Note that this is an unaggregated measure, returning the losses per observation.

Usage

linex(truth, response, a = -1, b = 1, ...)

Arguments

truth

(numeric())
True (observed) values. Must have the same length as response.

response

(numeric())
Predicted response values. Must have the same length as truth.

a

(numeric(1))
Shape parameter controlling asymmetry. Negative values penalize overestimation more, positive values penalize underestimation more. As a approaches 0, the loss resembles squared error loss. Default is -1.

b

(numeric(1))
Positive scaling factor for the loss. Larger values increase the loss magnitude. Default is 1.

...

(any)
Additional arguments. Currently ignored.

Value

Performance value as numeric(length(truth)).

Details

The Linear-Exponential Loss is defined as $$ b (\exp (t_i - r_i) - a (t_i - r_i) - 1), $$ where \(a \neq 0, b > 0\).

Meta Information

  • Type: "regr"

  • Range (per observation): \([0, \infty)\)

  • Minimize (per observation): TRUE

  • Required prediction: response

References

Varian, R. H (1975). “A Bayesian Approach to Real Estate Assessment.” In Fienberg SE, Zellner A (eds.), Studies in Bayesian Econometrics and Statistics: In Honor of Leonard J. Savage, 195–208. North-Holland, Amsterdam.

See also

Other Regression Measures: ae(), ape(), bias(), ktau(), mae(), mape(), maxae(), maxse(), medae(), medse(), mse(), msle(), pbias(), pinball(), rae(), rmse(), rmsle(), rrse(), rse(), rsq(), sae(), se(), sle(), smape(), srho(), sse()

Examples

set.seed(1)
truth = 1:10
response = truth + rnorm(10)
linex(truth, response)
#>  [1] 0.16093764 0.01794385 0.26923044 2.33443235 0.06077585 0.26069380
#>  [7] 0.14069596 0.35410244 0.20273828 0.04222553